The 20 million people in the United States at a given time figure is definitely too low.
According to Prevalence of Genital Human Papillomavirus Among Females in the United States, the National Health and Nutrition Examination Survey, 2003–2006 Journal of Infectious diseases (2011) vol. 204 pages 566-573.:
Overall prevalence of any HPV type as measured by HPV DNA positivity by the LA assay was 42.5% (95% CI, 40.3%–44.7%) among 14–59-year-old US females...this represents 39.5 million (95% CI, 37.4–41.5 million) noninstitutionalized females aged 14–59 years in the United States with prevalent HPV infection
53.8% of females age 20-24 tested positive for HPV.
Now can 80% in a life time be correct? A key point is this:
the prevalence of any HPV significantly increased after 14–19 years of age, peaking in young women 20–24 years of age. The observed age distribution in this study supports the body of epidemiologic evidence that suggests that first HPV infection is acquired shortly after a woman becomes sexually active [cites to references 20–22]. We also found that HPV prevalence continued to gradually but significantly decrease through 59 years of age. Age-related reductions in HPV prevalence are likely attributable to a variety of factors, including clearance over time, decreased incidence as a result of changes in sexual activity, and acquired immunity from previous infection.
In otherwords, without any treatment, people become no-longer infected with the virus. Therefore, significantly more women than the 53.8% will become infected at some point. See Mathematical Model for the Natural History of Human Papillomavirus
Infection and Cervical Carcinogenesis for more information about the rate at which the virus disappears from the body.
Furthermore, the 53.8% includes those who have never been sexually active.
Also, there are many different strains of HPV, and while the study tried to test for the major ones, testing 37 strains, there are still other strains that were not tested for.
Also, the study only tested for genital virus, there is also oral and anal HPV.
So yes, it seems very reasonable to estimate 80% for women.
For a specfic reference to the 80% number see the CDC report to congress Prevention of Genital Human Papillomavirus Infection which states
It has been estimated that at least 50% of sexually active men and women acquire genital HPV infection at some point in their lives; a recent estimate suggests that 80% of women will have acquired genital HPV by age 50 [cites to references 15 and 16]
The above part of the answer is really limited to HPV strains associated with sexual transmission.
A more recent study Human Papillomavirus Community in Healthy Persons, Defined by Metagenomics Analysis of Human Microbiome Project Shotgun Sequencing Data Sets J Virol. 2014 May; 88(9): 4786–4797 considered a broader spectrum of HPV strains than the earlier studies above.
148 strains of 176 known strains were explicitly considered in the study.
The overall HPV prevalence was 68.9% and was highest in the skin (61.3%), followed by the vagina (41.5%), mouth (30%), and gut (17.3%).
Considering this new study, if 69% of people have HPV detectable by the method of this study at a given moment, 80% in a lifetime is almost certainly an underestimate. The 80% number was based upon older studies that only detected a small percentage of the strains and sampled fewer regions of the body.